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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### Advanced mathematics

### For younger learners

# Noticing Patterns

### Summing Consecutive Numbers

### 1 Step 2 Step

### Pick's Theorem

### What's Possible?

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The key to solving these problems is to notice patterns or properties. Encouraging students to organise their work in a systematic way will allow them to notice what might not otherwise be obvious.

Age 11 to 14

Challenge Level

This problem offers a simple context for students to explore, make generalisations and prove conjectures, working numerically and algebraically.

Age 11 to 14

Challenge Level

This problem is inaccessible without looking at simpler cases, and thus helps students to see the value of specialising in order to generalise.

Age 14 to 16

Challenge Level

This problem allows students to consolidate their understanding of how to calculate the area of irregular shapes, while offering an opportunity to explore and discover an interesting result.

Age 14 to 16

Challenge Level

As well as introducing the difference of two squares, this problem allows students to explore, conjecture and use algebra to justify their results.